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JCT
2007
14 years 11 months ago
2007
We show that for any closed surface F with χ(F) −4 (or χ(F) −2), there exist graphs that triangulate the torus or the Klein bottle (or the projective plane) and that quadran...
113
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JCT
2008
14 years 10 months ago
2008
Let {a, b, c} be a triangle in a 3-connected matroid M. In this paper, we describe the structure of M relative to {a, b, c} when, for all t in {a, b, c}, either M\t is not 3-connec...
JCT
2006
14 years 12 months ago
2006
We prove that the Kazhdan-Lusztig polynomials are combinatorial invariants for intervals up to length 8 in Coxeter groups of type A and up to length 6 in Coxeter groups of type B a...
JCT
2006
14 years 12 months ago
2006
We give a new expression for the number of factorizations of a full cycle into an ordered product of permutations of specified cycle types. This is done through purely algebraic me...
JCT
2006
14 years 12 months ago
2006
One of Erdos' favourite conjectures was that any triangle-free graph G on n vertices should contain a set of n/2 vertices that spans at most n2/50 edges. We prove this when t...